Method and apparatus for controlling diameter in Czochralski crystal growth by measuring crystal weight and crystal-melt interface temperature

ABSTRACT

Diameter control in an apparatus and method for growing crystals using the Czochralski technique is accomplished by progressively measuring both the temperature of the melt by a heat sensor and the weight of the residue of the melt in the crucible by a suitable weighing device. The weight measurement data is fed to microprocessor having a control algorithm. The microprocessor output and temperature measurement output are fed to a three-term temperature controller which regulates the temperature of the melt to thereby control automatically the diameter of the crystal. The relationship between an error in weight and the amount of temperature regulation is varied in accordance with a desired weight.

Crystal growth by the Czochralski method has traditionally required thepresence of a skilled operator to watch the progress of a growingcrystal and to affect diameter changes by making appropriate adjustmentsto the temperature of the melt. The relationship between melttemperature and crystal diameter depends on a balance between the sum ofthe heat passing from the melt to the crystal plus the heat ofsolidification with the heat that can be conducted away from theinterface and lost to the environment. The qualitive relationship isthat a melt temperature increase will cause a decrease in crystaldiameter, but an exact relationship depends strongly on the existingcrystal size and shape and will change throughout a growth run. Toobtain good crystal quality it is necessary to maintain a constantgrowth rate as both stoichiometry and impurity concentration are growthrate sensitive. A closed loop servo type control over the crystaldiameter is thus desirable to obtain good quality crystals reproducibly.Additional reasons for automatic control are that growth runs may lastseveral hours to days making human supervision particularly tedious andthat often visibility of the growing crystal is impaired by, forinstance, thermal insulation in the growth chamber.

To achieve automatic control, some method of sensing the crystaldiameter must replace the operator's vision. Many methods have beenused, with that of weighing either the growing crystal or the melt pluscrucible being the most popular and widely applicable. Weighing thecrucible is mechanically simpler than weighing the crystal but crucibleweighing does suffer the disadvantage that levitation effects from ther.f. heating and evaporation losses from the melt can contribute to theweight signal. Such effects, however, can be taken account of in signalprocessing.

Methods of using the processed weight signal to produce an appropriateinfluence on melt temperature such as to achieve servo control over thediameter, are known. The best approach is to first differentiate theweight signal, the result of which should be constant for constantdiameter growth, and then compare this with an expected rate of changeof weight. The error signal thus obtained can be used in a standard wayto derive a control signal to adjust the melt temperature.

The electronic processing can be performed both by analogue and digitalmeans. The analogue methods are considerably less expensive whencompared with the cost of a mini-computer, but a digital control systemis much more powerful because it allows easy modifications to controlalgorithms even during a growth run.

The following specifications show details of known prior art in thisgeneral field:

British Pat. No. 1,465,191, National Research Development Corporationwhich uses an r.f. heater supply unit to provide a melt and includes aload cell and draw position indicator to achieve a regulated crystaldiameter by automatic means achieved through a system of heat control ordraw regulation.

British Pat. No. 1,494,342, National Research Development Corporationwhich has a load cell associated with the pull rod and uses adifferentiator and comparator.

Japanese Patent Specification No. 56-92195 Fujitsu K.K. et al, whichuses a load cell connected to a computer through an A.D. converter,which computer is also connected to a power control to regulate the r.f.heating current.

The object of the invention however is to provide an improved method ofand means for automatically producing crystals of a required diameterand this is achieved by measuring the temperature of the melt while alsomeasuring the loss of weight of the melt. A microprocessor processesboth factors to regulate the crystal growth conditions.

When the system, on which the present invention is based, is usedwithout automatic diameter control, a standard Czochralski crystalpuller is used, heating power to the crystal puller being provided by alow voltage industrial r.f. generator of say 50 kW capacity andoperating at a nominal frequency of perhaps 450 kHz. The usual powersources in Czochralski facilities operate at higher voltages and havethe power output controlled to a constant value by a closed loop systemwhich samples r.f. power, but in our system the power output iscontrolled so as to keep a constant melt or crucible temperature. Thisis achieved by sampling temperature with an optical pyrometer the outputof which is directed to an integrated three-term controller forcomparison with a temperature set-point. A standard 4-20 mA outputsignal from the controller actuates a motor adjusting the outputcoupling of the r.f. generator and hence the power transformed to thecrucible. The temperature at the monitoring point is controlled tobetter than 2° C. as indicated by the sensing head, and at thecrystal-melt interface to better than 1/3° C. as indicated by changes tocrystal diameter. The system has a response time of the order ofseconds. The manual operation of the facility requires a skilledoperator to observe the growing crystal and to obtain the desiredcrystal shape by making appropriate changes to the temperatureset-point.

Despite the excellence of the temperature control it is not practical toobtain automatic crystal growth by having the temperature set-pointfollow a predetermined programme for the following reasons:

(a) the complex relationship between temperature and crystal diameterdepending on already grown crystal size means that any slight deviationsin size during a run will invalidate a previously determinedtemperature-diameter measurement;

(b) the absolute temperature read by the sensor depends on theemissivity of the monitoring point and it is impractical to monitor theidentical point in different growth runs;

(c) it would take several runs to obtain a desired diameter-temperaturerelationship which would then be useless if any change in crystal shapewas required.

The automation of the Czochralski system according to this invention,using the weighing method of diameter control, has retained thetemperature control feature described above. The weight of the crucibleand melt is determined by an electronic balance, the digital output ofwhich is fed directly to a microprocessor which processes the signal,compares it to a preprogrammed value and produces a control signal toadjust the temperature set-point of the three-term controller. Controlof the melt temperature is still retained by the temperaturesensor/controller loop which copes with any short term fluctuations inthe r.f. power output.

The electronic balance used is preferably such that it is operated onthe 0-2000 g range with sensitivity of the digital weight measurement of0.1 of a gram. The balance is placed underneath the growth chamber andsupports the crucible plus melt and any additional thermal insulation.Some care is needed in setting the crucible assembly on top of theconnecting shaft to the balance, so that the shaft runs freely throughthe hole in the growth chamber. A locking nut allows the shaft plus itsload to be held for removal of the balance or to facilitate crucibleloading and also provides an air tight seal if purging of the atmosphereof the growth chamber is required prior to a growth run. Initial settingup also requires zeroing the balance by adding weights and using theelectronic zeroing facility, and then offsetting by an amount greaterthan the expected weight loss of the melt during the growth run bysimply adding such weight (typically 200 g) to the balance.

The invention is described with reference to the accompanying drawingsin which:

FIG. 1 is a block diagram showing the basic principle of the invention,

FIG. 2 is a transverse section of the mechanism for producing thecrystal,

FIG. 3 is a perspective view of a lithium niobate crystal grown with theautomatic diameter control, and

FIG. 4 shows a temperature-against-time graph of a typical growth run.

Referring first to FIG. 1, a chamber 1 has in it a crucible 2 containingthe melt 3 from which the crystal 4 is drawn by means of a seed 5 on apull-rod 6, the wall of the chamber 1 being supported on a chamber base7.

A rod 8 transfers the weight of the crucible 2 and melt to an electronicweighing device or balance 9, the output of which is fed to amicroprocessor 10.

The temperature of the melt 3 is sensed by an infrared temperaturesensor 11 through a window 12 in the wall of the chamber 1, and theoutput is passed to a three term controller 13 which is connected to aradio-frequency heating coil 14 surrounding the crucible 2 and melt 3.

The microprocessor 10 is connected to a terminal 15 and the output ofthe microprocessor 10 is fed through a digital analogue converter 16 tothe three term controller 13 so that the controller 13 is regulated byboth the output of the infrared temperature sensor 11 and the output ofthe electronic weighing device 9.

The mechanism is further described with reference to FIG. 2 from whichit will be seen that the crucible 3 is carried on a disc 20 secured tothe top of the rod 8 which passes through a guide 21 in the base 7 andcarries on it weights 22 to a selected value, the rod 8 transferring theweight of the crucible 2 and melt 3 together with its associatedmechanism to the electronic weighing device 9 which is supported on agranite or other stable block 23.

The disc 20 carries on it a sleeve 25 which surrounds the crucible 2,the space between the crucible 2 and the sleeve 25 being filled withalumina balls 26.

The sleeve 25 has an apertured disc 27 intermediate its ends throughwhich the crystal 4 is drawn, the space above the disc 27 having acylindrical wall 28 in it and the space between it and the sleeve 25 isfilled with thermal insulation 30.

TYPICAL FORM OF THE INVENTION

A digital display on the balance 9 indicates the weight, and accordingto this invention the output is made available in both digital andanalogue form. The analogue output of the weight is directed to a chartrecorder, not shown, and the digital signal is sent to themicroprocessor 10.

The microprocessor system used may be based on the Intel 8080 usingmainly Intel components. It is mounted on printed circuit cards whichare accommodated in a standard size card rack. The microprocessor 10 ispreferably located some four meters from the crystal growth chamber 1and r.f. generator to lessen the possibility of r.f. interference, andthe output from the balance is brought to the microprocessor 10 via ashielded cable and is fed onto the data bus by a 24-bit parallelinterface chip. The control signal output from the microprocessor, themelt temperature set-point, exits in 12-bit digital form via aninterface chip to a digital to analogue converter 16 (DAC). Thisproduces an analogue signal in the 0-10 V range which is fed directly tothe three-term controller 13.

The control software is stored in six EPROM'S (each 1K byte storage) and256 bytes of random access memory (RAM) is required for variable storageduring the running of the programme. The p.c. card system used for themounting of the micro-processor components is such that one EPROM cardwill accommodate 16K of memory and one RAM card will hold 8K. Anothercard holds the microprocessor chip and associated timing and systemcontrol devices. Two more cards complete the system, one holding the twoparallel I/O interface chips and the DAC and the other containing aserial I/O interface chip which connects to an external terminal forcommunication with a human operator.

BASIC THEORY OF THE WEIGHING METHOD

The relationship between the force experienced by a device monitoringthe crystal or melt weight and the crystal radius has been discussed byW. Bardsley, et al "The weighing Method of Automatic Czochralski CrystalGrowth" J. Cryst. Growth 40 (1977)--Ref 1--and by Van DiJk et al"Crystal diameter Control in Czochralski Growth" Acta Electronica 17,p45 (1974)--Ref 2--. As well as the force due to the mass of the crystalthere are extra effects due to the surface tension between melt andcrystal and buoyancy effects which depend on the position of the growthinterface in relation to the mean melt level. These extra effects areparticularly important in detecting changes in the crystal radius as aresponse to some melt temperature change. To appreciate the effects itis useful to restate some of the results of Ref 1. The force Fexperienced by the balance is the initial weight of the crucibleassembly plus melt, F_(o), less the weight of crystal pulled and theeffects due to the weight of the meniscus of melt supported and thesurface tension forces. ##EQU1## ρ_(s) and ρ_(L) are the respectivedensities of solid and liquid and r is the crystal radius at time t. his the height of the meniscus above the mean melt level and v is thecrystal growth rate related to the pull rate v_(o) by

    v=v.sub.o -h                                               (2)

where the dot denotes time derivative. The vertical component of surfacetension γ is related to the surface tension constant σ by

    γ=σ cos θ                                (3)

where the angle θ is the sum of the inclination of the crystal surface,θ_(s), and θ_(L), the angle of contact between solid and liquid whenwetting is not complete. The crystal inclination angle relates the rateof change of radius to the crystal growth rate

    tan θ.sub.s ×r/(v.sub.o -h)                    (4)

An expression for the meniscus height can be obtained theoretically andis

    h=[β(1-sin θ)+(β cos θ/4r).sup.2 ].sup.1/2 -β cos θ/4r                                            (5)

with

    β×2σ/ρ.sub.L g.                       (6)

For growth at a constant radius r_(o) the rate of change of weight ofthe crucible is given by

    F.sub.ref =-ρ.sub.s gπr.sup.2 v.sub.o               (7)

However if the crystal radius is changing there will be additional termsdue to the change in meniscus height and the surface tension forces asdescribed by equations (1) to (5) and these effects can be illustratedby linearising the equations with respect to the expected smalldeviation, a=r-r_(o), from the desired crystal radius. Equations (3),(4) and (5) become

    γ=γ.sub.o -γ.sub.θ θ.sub.S   (8)

    v.sub.o θ.sub.S =a                                   (9)

    h=h.sub.o +(h.sub.a /r.sub.o) a-h.sub.θ θ.sub.S (10)

Explicit expressions for the material constants γ_(o), γ.sub.θ, h_(o).h_(a) and h.sub.θ are given in Ref 1. Substituting (8), (9) and (10)into (1) gives the difference, E, between the actual rate of change ofweight of the crucible and the expected rate of change in terms of thedeviation from the expected radius

    E.tbd.F-F.sub.ref =-2πr.sub.o gρ.sub.s v(a+ηa-λa) (11)

with

    η=(2(ρ.sub.L h.sub.o +γ.sub.o /r.sub.o g)-(ρ.sub.s -ρ.sub.L) h.sub.a)/2ρ.sub.s v.sub.o               (12)

and

    λ=r.sub.o (2γθ/r.sub.o g-(ρ.sub.s -ρ.sub.L) h.sub.θ)/2ρ.sub.s v.sub.o.sup.2                 (13)

η and λ are material constants, η is always positive but λ depends morestrongly on the sign of ρ_(s) -ρ_(L) (ref 1). If the liquid is denserthan the solid (as it is for most semiconductors) then λ is positive.The dependence of the error in expected rate of weight change ondeviation of the crystal radius is complicated by the additional termsin a and a in equation (11). For example an increase in crystal radiusresults in an increased rate of change of weight of crystal given by thefirst term in (11). The second term is the same sign as the first andwould be beneficial in providing easier detection of a radius change byobserving the recordal weight. The third term however can be eithersign. If λ is negative (ρ_(s) >ρ_(L)) then a beneficial effect isobtained whereas if it is positive (ρ_(s) >ρ_(L)) it can sometimes swampthe first two terms and produce an error signal of the wrong sign. Thusan increase in radius may first show up as a decreased rate of change ofweight. The effect is due mainly to the well known fact that anincreasing radius first reduces the meniscus height and, if the liquidis denser than the solid, produces less effective crystal weight. Theanomaly is apparent with many semiconductor materials and is discussedfully with means of circumventing its effect in control applications inRef 1. However, in cases where ρ_(s) >ρ_(L), ρ is negative and the thirdterm adds to the other two providing extra signal for detecting radiuschanges.

The error signal as given by equation (11) can be used in a controlalgorithm to affect melt temperature changes to keep the crystal radiusto a desired value. Thus in response to an error in radius thetemperature of the melt is adjusted by ##EQU2## with E the rate ofweight change error as defined by equation (11). This is a typical"three-term" control function, with the parameters A, B and C to bechosen for optimum control. When (11) is used to relate E back tocrystal radius error it is seen that terms proportional to the radiuserror, its derivative and integral are present in ΔT but that there arealso some terms proportional to the second and third derivatives. Theselatter terms could be subtracted if they proved troublesome as they dofor example in the growth of semiconductors, see Bardsley et al "Theweighing method of Automatic Czochralski Crystal Growth ControlEquipment" J. Cryst. Growth 40, 21, (1977) Ref 3.

The optimum control parameters A, B and C can be determined by trial anderror methods on actual crystal growth runs or on numerically simulatedruns. Numerical simulation requires values for all the materialparameters used in equations (1) and (3) and in addition an expressiondescribing the time response of the crystal radius to a step change intemperature. Existing attempts at deriving such an expressiontheoretically (ref. 1) have of necessity used somewhat crudeapproximations and the result cannot be relied upon for quantative use.Experimental determination of the crystal response of temperature changeis straightforward for their particular situation. In the case of thegrowth of lithium niobate in the laboratory to be described laterherein, the control parameters were laboriously optimised during severalactual growth runs and this experience suggests that the development ofa numerical simulation model should be undertaken if major changes tothe growth situation are made which necessitate a reoptimisation of thecontrol parameters.

The implementation of the control algorithm in software for an 8080microprocessor was compiled on an IBM 370/168 computer for Intel's 8080Assembly language and Intel's PL/M, a high level language very similarto IBM's PL/1, but with modifications and restrictions applicable to8080 microprocessor use. The compilers reduced the higher level languagecodes to 8080 machine code which can be obtained as output on papertape. This code was then written from the tape onto EPROMS using amicroprocessor and locally available PROM programming hardware andsoftware.

Most of the control programme was written in PL/M which provides ease ofcoding for such things as arithmetic expressions, nested looping, use ofsubroutines and communication with the operator terminal. However onlyinteger arithmetic is allowed and care in coding to retain numericalprecision is required. A restriction is that arithmetic is unsignedwhich accounts for the repeated sign testing using the subroutine SIGNand duplication of coding.

The control programme has four distinct modes. The first is aninitialisation where the programme communicates with the operator,asking for input data about the crystal to be grown. After this theprogramme takes weight measurements, processes these and displays theaverage and derivative. At this time the operator inserts the seed intothe melt, noting contact by a sudden decrease in weight on the balance'sdigital display, and initiates growth, adjusting temperature until thecomputer printout shows the rate of change of weight to be a constantvalue appropriate to a small diameter crystal. The programme is thensent into the control mode and the crystal is grown automatically, withthe rate of weight change being controlled to a programmed referencevalue. The programme enters the completion mode when this referencevalue reaches zero and removes the crystal from the melt. A slow cooldown of the growth chamber then completes the run.

Communication with the operator terminal was in a form that would beintelligible to an operator not familiar with hexadecimal notation orthe programme details. Thus the programme sends prompting messages tothe terminal at the start of a growth run requesting data concerning thedesired crystal to be grown. The operator enters the data in ordinarydecimal notation which is converted to binary by the assembly languageroutine BCD2B. As the run proceeds output data is periodically relayedto the terminal for the operator's interest and includes current valuesof crucible weight in grams, the rate of change of weight in grams perhour, the reference rate of change, the error (EI), its derivative (FI),its integral (INT), a running average error (QI), the change made intemperature (PK), a temperature ramp value (R) and the currenttemperature set-point (TEMP). All, except the last three which are inhexadecimal, are in decimal notation with the assembly language routinesBCDOUT and B2BCD performing the output and conversion from binary. Muchof the communication with the terminal ultimately depends on routinesavailable in the Intel supplied SDK-80 Monitor programme which can becalled from the PL/M programme using small linking assembly languageroutines.

The weight signal from the electronic balance is in BCD format and isconverted to binary by the routine BCD2B. Sixteen readings are takenduring preset time intervals and averaged to give the average weightduring the interval. Timing is performed by counting machine cycles in asoftware loop and the time over which the weight is averaged is set bythe approximate response time of the crystal radius to a step change inmelt temperature. For the case to be described of the growth of lithiumniobate the response time was measured to be of the order of 12 min andweight averaging time was chosen to be two minutes. As the rate ofweight change is required for the error signal, the weight must bedifferentiated and this is accomplished by taking the slope of theleast-squares line of best fit through the most recent five weightreadings. If F₅ is the most recent weight then the least squares bestestimate of the slope is

    F=(2F.sub.5 +F.sub.4 -F.sub.2 -2F.sub.1)/10Δt

where Δt is the time interval of weight averaging. This procedurecoupled with the weight averaging greatly reduces noise in the signal tobe used for control but means that sudden real deviations of the crystalradius are not as readily detected. However this can be compensated forby using more derivative control as discussed later. The weightaveraging and storing of the most recent five averages is perfomed bythe software procedure AVERAGE and procedure W5421 gets theleast-squares best estimate of the differential weight.

At the completion of each weight averaging period when in the controlmode, a reference rate of change of weight is calculated, by theprocedure REFERENCE, based on input information about the desiredcrystal shape, the crystal pull-rate, crystal density and cruciblediameter. The programme allows for crystals with a constant diameterneck region (constant rate of weight change) followed by a linearincrease in rate of weight change (parabolic increase in radius) to themain diameter region which again has a constant rate of weight change.At the completion of growth at this diameter a linear decrease in rateof weight change describes a taper-in to zero diameter. Values for thereference rate of weight change in the constant neck region (GREF1) andfor the main diameter region (GREF2) are calculated at programmeinitialisation from the input data and the expression

    F.sub.ref =-πρ.sub.s v.sub.o R.sup.2 r.sup.2 /(R.sup.2 -r.sup.2)

where R is the crucible radius and enters the expression byconsideration of the drop in melt level. At each entry to REFERENCE acounter, STEPNO, is examined to see whether the crystal is in the NECK,TAPER, MAIN$LENGTH or FINAL$TAPER regions and the reference is set toGREF1, incremented by INC1 set to GREF2, or decremented INC2accordingly. INC1 and INC2 are calculated it programme initialisation toproduce the required changes in diameter in the specified length ofcrystal.

The control algorithm was originally based on that used by Zinnes et al"Automatic diameter control of Czochralski Grown Crystals" J. Cryst.Growth 19, 187(1973) Ref. 4 and employs much of their notation but inthe course of determining the optimum control parameters the algorithmwas also modified extensively. The following description is of the finalversion of the algorithm.

The error signal EI is the difference between the reference rate ofweight change of the crucible and the measured value. This is comparedwith a lower limit which is of the order of magnitude of the expectederror in the weight signal and a control signal is generated only if theabsolute value of EI is the greater. After some early trial runs it wasrecognised that strict proportional control was not appropriate, forinstance a one gram per hour error in the neck region of the crystalwhere the reference rate was say 1 g/hour, required more control actionthan a 1 g/hour error when the crystal was in the main diameter regionwith a 20 g/hour reference. However if control was made proportional tothe relative error and optimised for the neck region, then it would beinsufficient for the main diameter region. A suitable compromise was tovary the proportionality `constant` with the reference rate of weightchange as

    A=T.sub.1 /(a+bF.sub.ref)

Typical values as used for lithium niobate growth were a=1 g/hour,b=0.05 and T₁ =0.5° C. It was also found desirable to limit the maximumamount of control and this is conveniently done by making the maximumallowable error to be a+bF_(ref) such that for all errors greater thanthis the control is restricted to be T₁.

The derivative of the error signal FI is calculated simply as thedifference between the two previous errors and is not divided by thetime interval. As the control is applied in a single step after eachweight measuring interval the B constant (equation (14) is independentof time interval when the derivative is defined in this way. Theprevious discussion on the proportional control signal applies as wellto the derivative control signal, thus the maximum of the derivate islimited to a bF_(ref) and the B `constant` varies as T₂ /(a+bF_(ref)).

The integral is calculated as the sum of errors and is restricted to amaximum of F_(ref). However, when the error changes sign the integralreverts to zero, simulating the `anti-reset windup` facility in analoguecontrol systems. The multiplying factor to generate the integral controlsignal varies as the inverse of F_(ref),

    C=B.sub.2 /F.sub.ref

The parameter B₂ however will depend on the timing interval chosen.Although the facility for integral control has been retained in theprogramme it has not been required to date in actual crystal growthruns.

The temperature change, (PK in the programme listing), is calculated asthe ΔT in equation (14) and usually added to the temperature (TEMP) atthe end of each weight averaging period. It is possible to apply thechange in one step or gradually during the next weight averaging periodwith the option being offered at programme initialisation. Therelationship of the number in the computer representing temperature andthe real temperature is given by the procedure CONVERT. The computernumber varies from 0 to FFFF H. The 12 most significant bits of thisnumber are fed to the DAC which gives an analogue output of from 0 to 10V which can adjust the set-point of the IRCON controller over its fullrange. Thus a change of less than 8 to TEMP will not affect theset-point but a change of 10 H gives 0.36° C. change to the set-point.

When the reference rate of weight change reaches zero at the end of theFINAL$TAPER section the programme enters the completion mode via theprocedure REFERENCE. The pull-out strategy is to increase the melttemperature at a constant rate and monitor the weight until the rate ofchange is zero with zero derivative. The zero derivative requirement isimportant as the rate of change will go from negative to positive as thecrystal grows in and the meniscus height increases. This pull-outprocedure is very slow and often the actual pull-out has beenaccomplished by the operator manually increasing the lift rate after therate of weight change has been positive for some time. However, it wouldbe straightforward to have the microprocessor perform this increase oflift rate. Once the crystal is out of the melt the set-point is heldconstant for several minutes, the lift rate turned off and then thegrowth chamber slowly cooled by a programmed decrease in temperatureset-point.

Several means are available of interrupting the control programme duringa growth run. The most drastic of these is forcing a `reset` on themicroprocessor which then restarts at the beginning of the monitorprogramme at memory location 0. The peripheral interfaces are alsoreset, one effect of this being to send all the outputs high on thetemperature set-point output and giving a full-scale set-point, clearlya dangerous procedure if the system is in the automatic temperaturemode. A safer alternative is to use the external interrupt facilities ofthe microprocessor. A `request for interrupt` signal accompanied by anRST7 instruction, (all highs), on the data bus has no effect on theperipheral interfaces but restarts the microprocessor at memory location56 which contains a jump instruction in the SDK-80 monitor. The jump canbe to an interrupt processing routine which can finally return to thecontrol programme at the point of interruption and resume operation. Analternative to the interrupt processing routine is to jump back into themonitor programme which then stores current register values and allowsthe monitor functions to be used to examine and change control programmevariables stored in RAM. Another monitor function, obtained by enteringa G at the terminal, restarts the programme at the interrupted pointwith the altered variable values.

Two of the most common reasons for wanting to interrupt the controlprogramme are to change the temperature set-point, particularly duringthe seed insertion phase, and to cause an early but orderly terminationof the growth. Provision has been made in the software for interruptingfor these purposes, by having a check made periodically to see if acharacter is pending from the operator terminal. If so, procedureSET$POINT is invoked. If the character is a `T`, a new temperatureset-point can be entered in degrees C. and decimal notation. If thecharacter is an `F` then the step counter is made very large such thaton the next entry to REFERENCE the FINAL$TAPER section is begun todecrease the crystal diameter and terminate growth.

AUTOMATIC GROWTH OF LITHIUM NIOBATE CRYSTALS

Research into the crystal growth of lithium niobate had been conductedin this laboratory for some time and was beset with two major problems,these being a persistent brown coloration of the crystals and a verystrong probability of the boule cracking during cool down after growth.The cracking problem results from a combination of the large anisotropyin thermal expansion coefficients for lithium niobate and the structuralphase change at 1215° C., coupled with the excessive thermal gradientsin the crystal growth chamber usually associated with r.f. heating. Lowthermal gradients can be produced by considerable thermal insulation ofthe region immediately above the melt into which the crystal is pulled(`after-heating`) but two additional problems then arise as vision ofthe growing crystal is obstructed and the low thermal gradients make thecrystal diameter much more sensitive to melt temperature fluctuationsand therefore difficult to control. There is further evidence thatstraight sided boules are less prone to crack than boules grown withouttight diameter control. The brown coloration of the crystals is probablydue to niobium being in a lower valence state than the +5 required instoichiometric LiNbO₃. Possible reasons for this are that impurity metalions of +2 or higher valency have displaced lithium in the crystallattice or that there is a deficiency of oxygen in the crystal. Previousreports have indicated that annealing brown coloured lithium niobatecrystals in an oxygen atmosphere removes the colour and our experiencehas shown that lighter colour crystals result with good `after-heating`.The use of good `after-heating` together with the weighing method ofautomatic diameter control offered the possibility of solutions to allof the above problems and led to the development of the diameter controlsystem described in this report.

The experimental arrangement for the growth of lithium niobate wassimilar to that shown in FIGS. 1 and 2, with the balance weighing thewhole after-heater assembly as well as the crucible and melt. A pureplatinum crucible was used with growth temperatures of around 1300° C.,and oxygen was bled into the growth chamber at 2 l/min. Crystals werepulled at rates of 10 mm/hour and 5 mm/hour with the slower speed givingthe better results in terms of crack resistant crystals. Crystalrotation was 30 r/min. Seed orientations were either <111> or <310> inreciprocal rhombohedral coordinates. Starting chemicals were Optran zonerefined lithium niobate at the congruent melting composition.

Several trial growth runs were required to determine suitable values forthe control parameters. It was found that relatively large amounts ofderivative control were needed whereas integral control and the constantterm control were not required at all. The additional derivative controlresulting from the terms in a and a in equation (11) has thus beenbeneficial in this case. There has been no need to apply any correctionsfor effects of crucible levitation or melt evaporation. With the lowthermal gradients, the crystal diameter was very sensitive totemperature changes and as such, optimum values for the constants forproportional and derivative control were found to be T₁ =0.5° C. and T₂=1.0° C. such that the largest possible response to a radius error was a1.5° C. temperature change. The limitation on the maximum values oferror and derivative and the variation of the proportionality`constants` with reference rate of weight change was describedpreviously and the (unoptimised) values used gave maximum values forerror of 2 g/hour and 1 g/hour when the reference was 20 g/hour and 1g/hour respectively.

The degree of diameter control obtained under these condition istypified by the crystal shown in FIG. 3. In FIG. 4, a typicaltemperature profile for a crystal growth run is shown to illustrate howthe control strategy can achieve the long term large temperature changesnecessary for the given shape of crystal, while maintaining short termtight diameter control with temperature changes of the order of 1° C.

AUTOMATIC GROWTH OF CALCIUM TUNGSTATE CRYSTALS

Similar diameter control has been obtained on a crystal of calciumtungstate grown under conditions of low thermal gradients but at thenecessarily higher melt temperature of around 1650° C. No change wasrequired to the lithium niobate determined control parameters when theafter-heater was in position but these proved totally inadequate whenthe after-heater was not present. In this later case the crystaldiameter is much less sensitive to melt temperature changes and itappeared that a constant ramp term and an integral term would berequired together with larger constants for the proportional andderivative terms in the control function.

The use of a microprocessor for automatic diameter control in theCzochralski method provides the flexibility of computer control at lowcost. The capacity of the microprocessor has not been greatly taxed bythe application described here in terms of the data handling speed orprogramme storage space. It would be possible for the microprocessor tocontrol two or more crystal growing facilities at the same time as wellas monitoring various parts of the facilities as a safety precaution.

The application of automatic diameter control has solved a particularproblem with `after-heating` in the growth of lithium niobate but itsadditional advantage is in freeing staff from the tedious task ofcrystal watching.

The claims defining the invention are as follows:
 1. A method ofdiameter control in Czochralski crystal growth which comprises the stepsof:(a) drawing a crystal-forming material from a melt in a crucible at acontrolled rate and progressively measuring both the temperature of themelt and the weight of the residue of the melt in the crucible; (b)feeding the weight measurement data obtained according to step (a) to amicroprocessor of the type including a control algorithm to obtain anoutput; and (c) feeding the temperature measurement and themicroprocessor output to a threee term temperature controller whichregulates the temperature of the melt and thereby controls automaticallythe diameter of the crystal.
 2. A method of diameter control inCzochralski crystal growth comprising the steps of:(a) placing acrystal-forming material into a crucible in a heating zone; (b) applyingheat to the crucible to provide a melt of the crystal forming material;(c) mounting a seed on a rod positioned to dip the seed into the melt;(d) lifting the rod at a controlled rate to progressively draw acrystal; (e) progressively measuring the temperature of the melt with atemperature sensor; (f) progressively measuring the weight of the meltto determine rate of use of the melt and feeding the weight data soobtained to a microprocessor having a control algorithm; (g) feeding theoutput data of both the temperature sensor and the microprocessor to athree term heat controller; and (h) controlling the amount of heatapplied to said crucible by said applying step (b) with said heatcontroller to maintain automatically a controlled diameter during thelength of growth.
 3. The method of claim 2 wherein step (e) is practicedso the said temperature sensor operates in the infrared spectrum and isdirected to read the temperature at the interface between the melt andthe crystal being pulled.
 4. A device for growing a crystal usingCzochralski crystal growth comprising:a crucible adapted for receiving acrystal forming material; means defining a chamber, said crucibledisposed in said chamber; heating means, operatively coupled to saidchamber, for heating the crystal forming material contained in thecrucible to form a melt thereof; heat sensor means for progressivelyrecording the temperature of the melt in said crucible and forgenerating a temperature signal corresponding to the recordedtemperature; weighing means for progressively weighing the contents ofthe melt in the crucible and for generating a weight signalcorresponding to the weight of the melt; means for holding a seed andfor progressively drawing said seed upwards from the melt in thecrucible to form a crystal; data processing means, connected to saidweighing means, for receiving said weight signal as input from saidweighing means and for progressively converting said weight signal to aheat control factor; and three term controller means, operativelyconnected to said heat sensor means, said data processing means and saidheating means, for receiving said progressive temperature signal fromthe heat sensor means and the heat control factor from the dataprocessing means and for regulating the heat of the melt in response tosaid temperature signal and heat control factor to automaticallymaintain a selected diameter of the crystal.
 5. A device for controllingthe diameter of a crystal in Czochralski crystal growth comprising:athermally insulated chamber; a weighing platform in said chamber tosupport a crucible having a crystal forming material therein; rod meansprojecting into the said chamber for holding a crystal seed, said rodmeans including means for withdrawing the rod at a regulated rate;high-frequency means for heating crystal-forming material in response toa control signal to form a melt of said material in said crucible to bepositioned on said platform; an infrared temperature sensor meansdirected through a window in the said chamber for generating atemperature signal corresponding to the melt temperature; electronicweighing means for supporting at least the said platform and forgenerating a weight signal corresponding to the weight of the melt insaid crucible; comparator means, connected to said weighing means andreceiving said weight signal, for comparing the rate of change ofcrucible weight to preset values and for generating an output signalcorresponding to deviation from said preset values to effect appropriatetemperature changes; and controller means, operatively connected to saidtemperature sensor means, said high-frequency means and said comparatormeans and receiving both the temperature signal from said temperaturesensor means and the output signal from said comparator means, forproducing said control signal and for applying said control signal tosaid high-frequency means to thereby progressively control thetemperature of the melt in said crucible.
 6. Device according to claim 4wherein said heat sensor means is an infrared sensor directed toward theinterface between the melt and the crystal being formed.
 7. Deviceaccording to claim 5 wherein said temperature sensor means is directedtoward the interface between the melt and the crystal being formed.
 8. Adevice for controlling the diameter of a crystal during Czochralskicrystal growth comprising:means defining a chamber to house a cruciblecontaining a crystal-forming material; heating means for heating thecrystal-forming material to form a melt of said material in response toa control output signal; crystal forming means operatively associatedwith said chamber for forming a crystal and for withdrawing the crystalfrom the melt at a preselected rate; temperature sensor means forsensing the temperature of the melt in the crucible and for generating acorresponding temperature signal; weight sensing means for progressivelysensing the weight of the crucible and for progressively generating acorresponding weight signal; and control means, operatively connected tosaid heating means, said temperature sensor means and said weightsensing means, said control means including means for converting theprogressive weight signal to a rate signal corresponding to the rate ofcrucible weight change and comparing means for comparing said ratesignal to a preselected value to generate a comparison signalcorresponding to a deviation of said rate signal from said preselectedvalue, said control means for evaluating said deviation signal and saidtemperature signal, for responsively generating a control output signaland for applying said control output signal to said heating means, saidheating means controlling the temperature of the melt in said cruciblewhereby the diameter of the crystal being formed is controlled.